Stochastic dynamics of the magneto-optical trap

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed stochastic dynamics is described extensively. It is shown that it exists a variety of dynamical behaviors, which differ by the frequency components appearing in the dynamics. Indeed, some instabilities exhibit only low frequency components, while in other cases, a second time scale, corresponding to a higher frequency, appears in the motion of the center of mass of the cloud. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the existence of instabilities to folded stationary solutions where noise response is enhanced. The different types of regimes are explained by the existence of a relaxation frequency, which in some conditions is excited by noise.Received: 18 June 2003, Published online: 28 October 2003PACS: 32.80.Pj Optical cooling of atoms; trapping - 05.40.Ca Noise - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Large Cells in Poisson–Delaunay Tessellations

It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount from regularity, given that its volume is large. As a tool for the proof, a stability result for simplices is established.     

Ab initio study of the Fe intra- and inter-layer magnetic order in Fe/Ir(001) superlattices

We reconsider the semiconductor trions from scratch. We first determine the very many “reasonable” ways to write the trions in first quantization. We then select the forms which are easy to relate to physical pictures. In a second part, we derive the corresponding creation operators in second quantization. We pay particular attention to the expression of the X^- trion in terms of exciton and free-electron, as it is the one adapted to future works on many-body effects with trions. Received 27 May 2002 / Received in final form 18 December 2002 Published online 20 June 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

A Lattice Boltzmann model with high Reynolds number in the presence of external forces to describe microfluidics

We present here a lattice Boltzmann model with high Reynolds number in the presence of external force fields to describe electrokinetic phenomena in microfluidics, by considering pressure as the only external force for liquid flow. Our results from a 9-bit square lattice Boltzmann model are in excellent agreement with experimental data in pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The difference between the predicted and experimental Reynolds numbers from pressure gradients are well within 5%. Our results suggest that the lattice Boltzmann model described here is an effective computational tool to predict the more complex microfluidic systems that might be problematic using conventional methods.     

Evaluating a branch-and-bound RLT-based algorithm for minimum sum-of-squares clustering

Minimum sum-of-squares clustering consists in partitioning a given set of n points into c clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Sherali and Desai (JOGO, 2005) proposed a reformulation-linearization based branch-and-bound algorithm for this problem, claiming to solve instances with up to 1,000 points. In this paper, their algorithm is investigated in further detail, reproducing some of their computational experiments. However, our computational times turn out to be drastically larger. Indeed, for two data sets from the literature only instances with up to 20 points could be solved in less than 10 h of computer time. Possible reasons for this discrepancy are discussed. The effect of a symmetry breaking rule due to Plastria (EJOR, 2002) and of the introduction of valid inequalities of the convex hull of points in two dimensions which may belong to each cluster is also explored.     

Mathematical Models for Studying the Value of Motivational Leadership in Teams

Mathematical models are presented for studying the value of leadership in a team where the members interact with each other. The models are based on a leader’s role of motivating each team member to perform closer to his/her maximum ability. These models include controllable parameters whose values reflect the amount of task interdependence among the workers as well as the motivational skill and variability in the skill of the leader. Confirming results—such as the fact that the skill level of the leader is a critical factor in the expected performance of the team—establish credibility in the models. Mathematical analysis and computer simulations are used to provide new managerial insights into the value of the leader—such as the fact that the skill of the leader can be more important than controlling the amount of interdependence among the team members and that having a choice of multiple leaders with no particular motivating skill is beneficial to the performance of small teams but not to large teams.Daniel Solow received a B.S. in Mathematics from Carnegie-Mellon, an M.S. in Operations Research from the University of California at Berkeley, and a Ph. D. in Operations Research from Stanford University. He has been a professor at Case Western Reserve University since 1978. His research interests include complex systems, discrete, linear, and nonlinear optimization. He has also developed systematic methods for teaching mathematical proofs, computer programming, and operations research.Sandy Kristin Piderit is an assistant professor of organizational behavior at the Weatherhead School of Management at Case Western Reserve University, and earned her Ph.D. from the University of Michigan. She studies the roles of relationships among coworkers on their performance and satisfaction with their work environments, and has published studies in the Academy of Management Review, the Journal of Management Studies, and Management Science.Apostolos Burnetas received a Diploma in Electrical Engineering from National Technical University in Athens, Greece, and an M.B.A. and Ph.D. in Operations Research from Rutgers University. He has been at the Department of Operations at Case Western Reserve University and is currently an Associate Professor at the Department of Mathematics at the University of Athens. His research interests include stochastic models and optimization, complex systems, and applications in queueing systems, supply chain and the interface of operations with finance.Chartchai Leenawong received a B.S. in Mathematics from Chulalongkorn University in Bangkok, an M.S. in Computer Science from the Asian Institute of Technology in Bangkok, and a Ph.D. in Operations Research from Case Western Reserve University. His research interests include mathematical modeling of complex systems as applied to business organizations. He has been a professor at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand since 2002.     

A-posteriori error estimates for optimal control problems with state and control constraints

We discuss the full discretization of an elliptic optimal control problem with pointwise control and state constraints. We provide the first reliable a-posteriori error estimator that contains only computable quantities for this class of problems. Moreover, we show, that the error estimator converges to zero if one has convergence of the discrete solutions to the solution of the original problem. The theory is illustrated by numerical tests.     

Integrability of Analytic Almost Complex Structures on Banach Manifolds

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic Banach manifolds. With this result at hand, we extend some known results concerning existence of invariant complex structures on homogeneous spaces of Banach–Lie groups. By way of illustration, we construct the complex flag manifolds associated with unital C^*-algebras.Mathematics Subject Classifications (2000): primary 32Q60; secondary 53C15, 58B12.     

Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.